In making a multilayered heat-sealable object having a heat-sealing layer on a structural layer, one is confronted with the problem that, as the composition of the layer is modified to improve heat-sealing properties, the object may become undesirably sticky at exposed areas that are not heat-sealed. The heat-sealing layer may also have other properties making it undesirable for an exposed layer; e.g., an ethylene-vinyl acetate copolymer layer can generate acetic acid when subjected to sterilizing methods such as radiation and autoclaving, and, if the layer is facing the interior of a bag, the generated acetic acid could contaminate the contents of the bag.